Homework 5B1545 Time series analysis

Homeworks

The homeworks should preferrably be done in groups consisting of three persons. You are however permitted to work alone or in pair or occasionally in groups of four persons.

Results on homeworks is found here.

In addition to the general there is four homeworks. Here is a link to data sources that can be used for the general homework

In the homeworks you are recommended to use MATLAB. A lot of m-files are found in this page. In the book of Brockwell and Davis follows a disk with their time series program PEST. A nice Windows version can be downloaded from this place. It is a zip-file (853 kB) to be extracted in a appropriate directory. Try it if you want to, it is easy to use.

To save a file from the browser, click the right knob of your mouse and save the file at an appropriate place.

The data-files for all homeworks (except the general one) are compressed in this zip-file. Save it and decompress it. The data appear both in readable ASCII-files and in MATLAB mat-files. The m-files you need are all compressed in this zip-file. Decompress also this file.

The first homework use the following m-files

acf.m ( sample autocorrelations function)
acvf.m (sample auto covarians function)
diffd.m (differensoperator)
ljungbox.m (Ljung-Box test)
ranktest.m (Rank test for independence)
seascomp.m (seasonal component)
smoothma.m (Moving average smoothing)
smoothpf.m (polynomial fitting)

The data is found insealevel.dat orsldate.dat or in the MATLAB data file sealevel.mat.

The second homework, use the following m-files

armaacvf.m (autocovariance function for ARMA process)
arroots (gives roots of AR generating function)
causal.m (tells if the process is causal)
innov.m (innovation algorithm used in predarma)
predarma.m (prediction of ARMA process)
psi.m (psi coefficients in linear representaton)
roots2ar (gives AR parameters from generating function roots)
simarma.m ( simulation of ARMA process)

The acf.m and acvf.m files should also be used. Just click on the links and save the files in an appropriate place. The m-file plotbar.m can be helpful when drawing autocorrelation function as bars from the x-axis. It is similar to the standard m-file stem which draws bars ending with circles.

The third homework,

boxcox.m

boxcoxf.m (function of Box-Cox transformation)
burg.m (Burg estimation AR process)
mlest.m (ML estimation of ARMA process, does not work in MATLAB 6)
mlest6.m (ML estimation of ARMA process för MATLAB 6)
pacf.m (Partial autocorrelation function, PACF)
pergram.m (periodogram)
specarma.m (spectral density ARMA process)
specdens.m (spectral density stationary process)
yuwaest.m (Yule-Walker estimation, AR-process)

The data are found in armadata.dat , temp.dat,timech.datandel.dator all together in the MATLAB data file data3.mat. . The matlab command 'load data3' will load them into a MATLAB session.
The m-file read3.m ( reads the dat-files into Matlab. Which row to use in the file armadata, see the result page Rutinerna för maximum-likelihoodskattningen (mlest) kräver Identification Toolbox som inte finns i KTH-CDn.

The fourth homework, homework 4, use the following m-files

archsim.m (simulate an ARCH(1) process)
garchsim.m(simulate a GARCH(1,1) process)
prctile.m (comuptes a given percentile in a data set)
garchpq.m(estimation of GARCH(p,q) process)
garchlikelihood.m(likelihood function GARCH(p,q) process)
garchcore.m(calculations in GARCH(p,q) process)
garchgrad.m(gradient used for searching in GARCH(p,q) process)

The MATLAB data file is found in logret_DEM_USD.mat . Here the same data in a text-file, logret_DEM_USD.dat.

The four last m-files comes from a toolbox made by Kevin Sheppard.

Rutinerna för garch-estimering kräver Optimization Toolbox som inte finns i KTH-CDn.

If you have problems to get the files, tell me at e-mail enger@math.kth.se or telephone 790 7134.

Last change 2004-10-26